Windows of given area with minimal heat diffusion

DOI10.1090/S0002-9947-99-02207-2zbMath0953.49035MaRDI QIDQ4219172

Jochen Denzler

Publication date: 18 November 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

optimal shapevariational problemspherical symmetrization

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for second-order elliptic equations (35J20)

Related Items (16)

Converse Symmetry and Intermediate Energy Values in Rearrangement Optimization Problems ⋮ An optimal insulation problem ⋮ Optimization problems with fixed volume constraints and stability results related to rearrangement classes ⋮ The Brezis-Nirenberg problem for the fractional Laplacian with mixed Dirichlet-Neumann boundary conditions ⋮ On the best Sobolev trace constant and extremals in domains with holes ⋮ A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems ⋮ A shape optimization problem for Steklov eigenvalues in oscillating domains ⋮ Optimal boundary holes for the Sobolev trace constant ⋮ Principal eigenvalue of mixed problem for the fractional Laplacian: moving the boundary conditions ⋮ Rearrangements and minimization of the principal eigenvalue of a nonlinear Steklov problem ⋮ Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond ⋮ Perturbation of eigenvalues due to gaps in two-dimensional boundaries ⋮ A constrained shape optimization problem in Orlicz-Sobolev spaces ⋮ SYMMETRY AND SYMMETRY BREAKING FOR MINIMIZERS IN THE TRACE INEQUALITY ⋮ Lifshitz tails for quantum waveguides with random boundary conditions ⋮ An optimization problem in thermal insulation with Robin boundary conditions

Cites Work

• Spherical symmetrization and eigenvalue estimates
• The Neumann problem for elliptic equations with non-smooth coefficients
• Bounds for the heat diffusion through windows of given area
• Zur Symmetrisierung von Funktionen auf Sphären
• A general rearrangement inequality for multiple integrals
• Linear and quasilinear elliptic equations
• Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni hölderiane
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• The Neumann problem on Lipschitz domains
• Elliptic Partial Differential Equations of Second Order
• Die Brunn‐Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie. I
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Windows of given area with minimal heat diffusion